An approach to the evaluation of multivariate data during ball end milling free-form surface fragments

• Fragments were taken from free-form surfaces to measure surface roughness and surface error.
• Tool edge micro-geometry was measured to check tool wear progress.
• The sequence of process planning – down milling, linear strategy and downward direction of milling – was determined.
• Effect of the signed radii on surface roughness was identified.
• Khattree–Naik’s plot shows a link between process geometry and measurement.

We present a method for investigating the process of ball end milling, a technology widely used in tool making and moulding. We analyse the main features of free-form surfaces used in this technology, and propose a sequence of steps to identify the most suitable milling strategy. The basic idea of such a sequence lies in the definition of the tangible fragments of free-form surfaces applicable to tool making. Tangible fragments represent the parts of tooling and signed radii that can distinguish both the active and transitional surfaces of tooling. Free-form surface fragments were selected since they are capable of securing definiteness in measurement of roughness parameters and surface errors. We investigated the operation capability of solid ball end milling cutters in terms of cutting tool edge micro-geometry. Cutting edge radius (rn) and roughness parameters of the tool edge were measured to determine the relationship between new and worn tool edges. Roughness parameters were measured at different parts of the machined surfaces, which take on typical features of dies and moulds, such as inclined wall, ridge lines, valley lines, as well as, the active surfaces defined by signed radii. Surface error such as scallop height, gouging, tolerances and actual signed radii were measured at transitive surfaces. The traditional approach of evaluating roughness parameters was used to determine the suitability of factors such as milling operation, milling strategy and direction of milling. In addition, traditional approaches such as relationships, distributions and histograms were also used. We applied Khattree–Naik’s plot, which proves its suitability to visualise all the data being measured in the same units: microns and millimetres. Characteristic features of the ball end milling process, such as tool edge micro-geometry, geometry of the machined surface, and unit length of the transitive surface were applied in Khattree–Naik’s plots. We found that this plot was capable of processing multivariate data to distinguish specific markers of the quality of machined surfaces, which are produced in ball end milling.